@article{arnold2016efficient,
author={Taylor Arnold and Ryan J. Tibshirani},
title={Efficient implementations of the generalized lasso dual path algorithm},
journal={Journal of Computational and Graphical Statistics},
volume={25},
number={1},
pages={1--27},
year={2016},
}

@book{gill1986user,
title={User's guide for LSSOL (version 1.0): A FORTRAN package for constrained linear least squares and convex quadratic programming},
author={Gill, P.E. and Hammarling, S.J. and Murray, W. and Saunders, M.A. and Wright, M.H.},
year={1986},
publisher={Systems Optimization Laboratory, Department of Operations Research, Stanford University}
}

@article{igraph,
title = {The igraph software package for complex network research},
author = {Gabor Csardi and Tamas Nepusz},
journal = {InterJournal},
volume = {Complex Systems},
pages = {1695},
year = {2006},
url = {http://igraph.sf.net},
}

@Manual{limSolve,
title = {limSolve: Solving Linear Inverse Models},
author = {Karline Soetaert and Karel Van den Meersche and Dick van Oevelen},
year = {2012},
note = {R package version 1.5.3},
url = {http://CRAN.R-project.org/package=limSolve},
}


@article{barrodale1978efficient,
title={An efficient algorithm for discrete l 1 linear approximation with linear constraints},
author={Barrodale, I. and Roberts, FDK},
journal={SIAM Journal on Numerical Analysis},
pages={603--611},
year={1978},
publisher={JSTOR}
}

@book{statshd,
author={Peter Buhlmann and Sara van der Geer},
title={Statistics for High-Dimensional Data},
publisher={Springer-Verlag},
address={Berlin},
year=2011,
}

@article{persist,
author={Eitan Greenshtein and Ya'acov Ritov},
title={Persistence in high-dimensional linear predictor selection and the virtue of overparametrization},
journal={Bernoulli},
volume=10,
number=6,
pages={971--988},
year=2004,
}

@article{mcplus,
title={Nearly unbiased variable selection under minimax concave penalty},
author={Cun-Hui Zhang},
journal={Annals of Statistics},
volume=38,
number=2,
pages={894--942},
year=2010,
}

@article{tracelasso,
title={Trace lasso: a trace norm regularization for correlated designs},
author={Edouard Grave and Guillaume Obozinski and Francis Bach},
journal={Advances in Neural Information Processing Systems},
volume=24,
year=2011,
}

@article{neariso,
title={Nearly-isotonic regression},
author={Ryan J. Tibshirani and Holger Hoefling and Robert Tibshirani},
journal={Technometrics},
volume=53,
number=1,
pages={54--61},
year=2011,
}

@article{adaptlasso,
title={The adaptive lasso and its oracle properties},
author={Hui Zou},
journal={Journal of the American Statistical Association},
volume=101,
number=476,
pages={1418--1429},
year=2006,
}

@article{ds,
title={The {Dantzig} selector: statistical estimation when $p$ is much larger than $n$},
author={Emmanuel J. Candes and Terence Tao},
journal={Annals of Statistics},
volume=35,
number=6,
pages={2313--2351},
year=2007,
}

@article{shao,
title={An asymptotic theory for linear model selection},
author={Jun Shao},
journal={Statistica Sinica},
volume=7,
number=2,
pages={221--264},
year=1997,
}

@article{scadtune,
title={Tuning parameter selectors for the smoothly clipped absolute deviation method},
author={Hansheng Wang and Runze Li and Chih-Li Tsai},
journal={Biometrika},
volume=94,
number=3,
pages={533--568},
year=2007,
}

@article{admm,
title={Distributed Optimization and Statistical Learning via the Alternative Direction Method of Multipliers},
author={Steve Boyd and Neal Parikh and Eric Chu and Borja Peleato and Jonathan Eckstein},
journal={Foundations and Trends in Machine Learning},
volume=3,
number=1,
pages={1--122},
year=2010,
}

@article{fista,
title={A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems},
author={Amir Beck and Marc Teboulle},
journal={SIAM Journal on Imaging Sciences},
volume=2,
number=1,
pages={183--202},
year=2009,
}

@article{locadapt,
author={Enno Mammem and Sara van de Geer},
title={Locally apadtive regression splines},
journal={Annals of Statistics},
volume=25,
number=1,
pages={387--413},
year=1997,
}

@unpublished{convgeom,
author={Venkat Chandrasekaran and Benjamin Recht and Pablo A. Parrilo and Alan S. Willsky},
title={The convex geometry of linear inverse problems},
note={arXiv: 1012.0621},
year=2010,
}

@unpublished{unifmest,
author={Sahand Negahban and Pradeep Ravikumar and Martin J. Wainwright and Bin Yu},
title={A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers},
note={To appear in Statistical Science},
year=2012,
}

@article{enumpoly,
author={Komei Fukuda and Thomas M. Liebling and Francois Margot},
title={Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron},
journal={Computational Geometry: Theory and Applications},
volume=8,
number=1,
pages={1--12},
year=1997,
}

@unpublished{larscomp,
author={Julien Mairal and Bin Yu},
title={Complexity Analysis of the Lasso Regularization Path},
year=2012,
note={arXiv: 1205.0079},
}

@article{donmost,
author={David L. Donoho},
title={For most large underdetermined systems of linear equations, the minimal $\ell_1$ solution is also the sparsest solution},
journal={Communications on Pure and Applied Mathematics},
volume=59,
number=6,
pages={797--829},
year=2006,
}

@article{dossal,
author={Charles Dossal},
title={A necessary and sufficient condition for exact sparse recovery by $\ell_1$ minimization},
journal={Comptes Rendus Mathematique},
volume=350,
number={1--2},
pages={117--120},
year=2012,
}

@unpublished{dfl1v1,
author={Charles Dossal and Maher Kachour and Jalal Fadili and Gabriel Peyre and Christophe Chesneau},
title={The degrees of freedom of penalized $\ell_1$ minimization},
year=2011,
note={arXiv: 1111.1162, v1},
}

@article{persistence,
title={Persistence in high-dimensional linear predictor selection and the virtue of overparametrization},
author={Eitan Greenshtein and Ya'Acov Ritov},
journal={Bernoulli},
volume=10,
number=6,
pages={971--988},
year=2004,
}

@article{irrepcond,
title={On Model Selection Consistency of Lasso},
author={Peng Zhao and Bi Yu},
journal={Journal of Machine Learning Research},
volume=7,
pages={2541--2564},
year=2006,
}

@article{fuchs,
author={Jean Jacques Fuchs},
title={Recovery of exact sparse representations in the presense of bounded noise},
journal={IEEE Transactions on Information Theory},
volume=51,
number=10,
pages={3601--3608},
year=2005,
}

@article{nearopt,
author={Emmanuel J. Candes and Terence Tao},
title={Near optimal signal recovery from random projections: {U}niversal encoding strategies?},
journal={IEEE Transactions on Information Theory},
volume=52,
number=12,
pages={5406--5425},
year=2006,
}

@article{cs,
author={David L. Donoho},
title={Compressed Sensing},
journal={IEEE Transactions on Information Theory},
volume=52,
number=12,
pages={1289--1306},
year=2006,
}

@article{sharp,
author={Martin J. Wainwright},
title={Sharp thresholds for high-dimensional and noisy sparsity recovery using $\ell_1$-constrained quadratic programming (lasso)},
journal={IEEE Transactions on Information Theory},
volume=55,
number=5,
pages={2183--2202},
year=2009,
}

@article{nearideal,
author={Emmanuel J. Candes and Yaniv Plan},
title={Near ideal model selection by $\ell_1$ minimization},
journal={Annals of Statistics},
volume=37,
number=5,
pages={2145--2177},
year=2009,
}

@article{faceenum,
author={Komei Fukuda and Thomas M. Liebling and Francois Margot},
title={Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron},
journal={Computational Geometry},
volume=8,
number=1,
pages={1--12},
year=1997,
}

@article{scad,
author={Jianqing Fan and Runze Li},
title={Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties},
journal={Journal of the American Statistical Association},
volume=96,
number=456,
pages={1348--1360},
year=2001,
}

@article{loubes,
author={Jean-Michel Loubes and Pascal Massart},
title={Dicussion to ``{L}east Angle Regression''},
journal={Annals of Statistics},
volume=32,
number=2,
pages={460--465},
year=2004,
}

@unpublished{lassodf2,
author={Ryan J. Tibshirani and Jonathan Taylor},
title={Degrees of Freedom in Lasso Problems},
note={To appear, Annals of Statistics},
year=2012,
}

@book{rockafellar,
author={R. Tyrrell Rockafellar},
title={Convex Analysis},
publisher={Princeton University Press},
address={Princeton},
year=1970,
}

@article{boostpath,
author={Saharon Rosset and Ji Zhu and Trevor Hastie},
title={Boosting as a regularized path to a maximum margin classifier},
journal={Journal of Machine Learning Research},
volume=5,
pages={941--973},
year=2004,
}

@article{gorman,
author={J. W. Gorman and R. J. Toman},
title={Selection of variables for fitting equations to data},
journal={Technometrics},
volume=8,
number=1,
pages={27--51},
year=1966,
}

@book{grunbaum,
title={Convex Polytopes},
author={Branko Grunbaum},
note={Second edition},
publisher={Springer-Verlag},
address={New York},
year=2003,
}

@PhdThesis{ryanphd,
title={The Solution Path of the Generalized Lasso},
author={Ryan J. Tibshirani},
school={Department of Statistics, Stanford University},
year={2011},
}

@article{bradbiased,
title={How biased is the apparent error rate of a prediction rule?},
author={Bradley Efron},
journal={Journal of the American Statistical Association: Theory and Methods},
volume=81,
number=394,
pages={461--470},
year=1986,
}

@article{mallows,
title={Some comments on {$C_p$}},
author={Colin Mallows},
journal={Technometrics},
volume=15,
number=4,
pages={661--675},
year=1973,
}

@article{sparsenet,
author={Rahul Mazumder and Jerome Friedman and Trevor Hastie},
title={{S}parse{N}et: Coordinate Descent with Nonconvex Penalties},
journal={Journal of the American Statistical Association},
volume=106,
number=495,
pages={1125--1138},
year=2011,
}

@book{esl,
author={Hastie, Trevor and Tibshirani, Robert and Friedman, Jerome},
title={The Elements of Statistical Learning; Data Mining, Inference and Prediction},
note={Second edition},
publisher={Springer-Verlag},
address={New York},
year=2008,
}

@article{genlasso,
title={The Solution Path of the Generalized Lasso},
author={Ryan J. Tibshirani and Jonathan Taylor},
journal={Annals of Statistics},
volume =39,
number=3,
pages={1335--1371},
year=2011,
}

@unpublished{genlasso-supp,
author={Tibshirani, Ryan J. and Taylor, Jonathan},
title={Proofs and Technical Details for ``{T}he Solution Path of the Generalized Lasso''},
url={\url{http://www.stat.cmu.edu/~ryantibs/papers/genlasso-supp.pdf}},
year=2011,
}

@article{tisp,
author={Yiyuan She},
title={Sparse regression with exact clustering},
journal={Electronic Journal of Statistics},
volume=4,
pages={1055--1096},
year=2010
}

@article{dasso,
author={Gareth M. James and Peter Radchenko and Jinchi Lv},
title={{DASSO}: connections between the {D}antzig selector and lasso},
journal={Journal of the Royal Statistical Society: Series B},
volume=71,
number=1,
pages={127--142},
year=2009
}

@misc{h1n1,
author={{Centers for Disease Control and Prevention}},
title={Novel {H1N1} Flu Situation Update},
year=2009,
url={\url{http://www.cdc.gov/h1n1flu/updates/061909.htm}},
}

@manual{cran,
author={{R Development Core Team}},
title={R: A Language and Environment for Statistical Computing},
organization={R Foundation for Statistical Computing},
address={Vienna, Austria},
year=2008,
note={{ISBN} 3-900051-07-0},
url={\url{http://www.R-project.org}},
}

@article{glmnet,
author={Jerome Friedman and Trevor Hastie and Robert Tibshirani},
title={Regularization paths for generalized linear models via coordinate descent},
journal={Journal of Statistical Software},
volume=33,
number=1,
pages={1--22},
year=2010
}

@book{gam,
author={Trevor Hastie and Robert Tibshirani},
title={Generalized additive models},
publisher={Chapman and Hall},
address={London},
year=1990,
}

@article{avs,
author={Michael Elad and Peyman Milanfar and Ron Rubinstein},
title={Analysis versus synthesis in signal priors},
journal={Inverse problems},
volume=23,
number=3,
pages={947--968},
year=2007,
}

@book{splines,
author={Carl de Boor},
title={A practical guide to splines},
publisher={Springer-Verlag},
address={New York},
year=1978,
}

@unpublished{parqp,
author={Michael J Best},
title={An algorithm for the solution of the parametric quadratic programming problem},
note={CORR Report 82--84, University of Waterloo},
year=1982,
}

@article{owenoutlie,
author={Yiyuan She and Art B. Owen},
title={Outlier Detection Using Nonconvex Penalized Regression},
journal={Journal of the American Statistical Association: Theory and Methods},
volume=106,
number=494,
pages={626--639},
year=2011,
}

@article{mccann,
title={Robust variable selection using least angle regression an elemental set sampling},
author={Lauren McCann and Roy Welsch},
journal={Computational Statistics \& Data Analysis},
volume=52,
number=1,
pages={249--257},
year=2007,
}

@article{gannaz,
title={Robust estimation and wavelet thresholding in partially linear models},
author={Irene Gannaz},
journal={Statistics and Computing},
volume=17,
number=4,
pages={293--310},
year=2007,
}

@unpublished{holger,
author={Holger Hoefling},
title={A path algorithm for the fused lasso signal approximator},
note={Unpublished},
url={\url{http://www.holgerhoefling.com/Articles/FusedLasso.pdf}},
year=2009,
}

@incollection{lrm,
author={Cleveland, W.S. and Grosse, E. and Shyu, W. and Terpenning, I.},
title={Local regression models},
booktitle={Statistical models in {S}},
publisher={Wadsworth},
address={Belmont},
editor={Chambers, J. and Hastie, T.},
year=1991,
}

@article{vcm,
title={Varying-coefficient models},
author={Trevor Hastie and Robert Tibshirani},
journal={Journal of the Royal Statistical Society: Series B},
volume=55,
number=4,
page={757--796},
year=1993,
}

@article{agri,
title={Crop production and soil salinity: evaluation of field data from {I}ndia by segmented linear regression},
author={R.J. Oosterbaan and D.P. Sharman and K.N. Singh and K.V.G.K. Rao},
journal={Proceedings of the Symposium on Land Drainage for Salinity Control in Arid and Semi-Arid Regions},
volume=3,
number={V},
pages={373--383},
year=1990,
}

@article{gbm,
title={High-resolution genome-wide mapping of genetic alterations in human glial brain tumors},
author={M. Bredel and C. Bredel and D. Juric and G.R. Harsh and H. Vogel and L.D. Recht and B.I. Sikic},
journal={Cancer Research},
volume=65,
number=10,
pages={4088--4096},
year=2005,
}

@article{relax,
title={Relaxed Lasso},
author={Nicolai Meinshausen},
journal={Computational Statistics \& Data Analysis},
volume=52,
issue=1,
pages={374--393},
year=2007,
}

@article{doncount,
title={Counting faces of randomly-projected hypercubes and orthants, with applications},
author={David L. Donoho and Jared Tanner},
journal={Dicrete and Computational Geometry},
volume=43,
number=3,
pages={522--541},
year=2010,
}

@article{tv,
title={Nonlinear total variation based noise removal algorithms},
author={Leonid I. Rudin and Stanley Osher and Emad Faterni},
journal={Physica {D}: Nonlinear Phenomena},
volume=60,
pages={259--268},
year=1992,
}

@article{rosset,
title={Piecewise linear regularized solution paths},
author={Saharon Rosset and Ji Zhu},
journal={Annals of Statistics},
volume=35,
number=3,
pages={1012--1030},
year=2007,
}

@article{homotopy1,
title={A new approach to variable selection in least squares problems},
author={Michael Osborne and Brett Presnell and Berwin Turlach},
journal={IMA Journal of Numerical Analysis},
volume=20,
number=3,
pages={389--404},
year=2000,
}

@article{homotopy2,
title={On the lasso and its dual},
author={Michael Osborne and Brett Presnell and Berwin Turlach},
journal={Journal of Computational and Graphical Statistics},
volume=9,
number=2,
pages={319--337},
year=2000,
}

@PhdThesis{holgerphd,
title={Topics in machine learning},
author={Holger Hoefling},
school={Department of Statistics, Stanford University},
year=2009,
}

@article{enet,
title={Regularization and variable selection via the elastic net},
author={Hui Zou and Trevor Hastie},
journal={Journal of the Royal Statistical Society: Series B},
volume=67,
number=2,
pages={301--320},
year=2005,
}

@book {ziegler,
author={Ziegler, Gunter M.},
title={Lectures on polytopes},
series={Graduate Texts in Mathematics},
publisher={Springer-Verlag},
address={New York},
volume=152,
pages={x+370},
year=1995,
isbn={0-387-94365-X},
mrclass={52Bxx},
mrnumber={MR1311028 (96a:52011)},
mrreviewer={Margaret M. Bayer},
}

@book{gvl,
title={Matrix computations},
author={Gene H. Golub and Charles F. {Van Loan}},
publisher={The Johns Hopkins University Press},
address={Baltimore},
note={Third edition},
year=1996,
}

@book{evans,
title={Measure theory and fine properties of functions},
author={Lawrence Evans and Ronald Gariepy},
publisher={CRC Press},
address={Boca Raton},
year=1992,
}

@book{schneider,
title={Convex bodies: the {B}runn-{M}inkowski theory},
author={Rolf Schneider},
publisher={Cambridge University Press},
address={Cambridge},
year=1993,
}

@article{nesterov,
title={Smooth minimization of non-smooth functions},
author={Yurii Nesterov},
journal={Mathmetical Programming},
volume=103,
number=1,
pages={127--152},
year=2005,
}

@article{bp,
title={Atomic decomposition for basis pursuit},
author={Scott Chen and David L. Donoho and Michael Saunders},
journal={SIAM Journal on Scientific Computing},
volume=20,
number=1,
pages={33--61},
year=1998,
}


@article{nesta,
title={{NESTA}: A fast and accurate first-order method for sparse recovery},
author={Stephen Becker and Jerome Bobin and Emmanuel J. Candes},
journal={SIAM Journal on Imaging Sciences},
volume=4,
number=1,
pages={1--39},
year=2011,
}

@unpublished{fusedp,
title={A Dynamic Programming algorithm for the Fused Lasso and $L_0$-segmentation},
author={Nicholas Johnson},
note={To appear in JCGS},
year=2009,
}

@article{cgh,
title={Microarray analysis reveals a major direct role of {DNA} copy number alteration in the transcriptional program of human breast tumors},
author={J.R. Pollack and T. Sorlie and C.M. Perou and C.A. Rees and S.S. Jeffrey and P.E. Lonning and R. Tibshirani and D. Botstein and A.L. Borresen-Dale and P.O. Brown},
journal={Proceedings of the National Academy of Science},
volume=99,
number=20,
pages={12963--12968},
year=2002,
}

@article{svmpath,
title={The entire regularization path for the support vector machine},
author={Trevor Hastie and Saharon Rosset and Robert Tibshirani and Ji Zhu},
journal={Journal of Machine Learning Research},
volume=5,
pages={1391--1415},
year=2004,
}

@article{glmpath,
title={$L_1$-regularization path algorithm for generalized linear models},
author={Mee Young Park and Trevor Hastie},
journal={Journal of the Royal Statistical Society: Series B},
volume=69,
number=4,
pages={659--677},
year=2007,
}

@article{grouplasso,
title={Model selection and estimation in regression with grouped variables},
author={Ming Yuan and Yi Lin},
journal={Journal of the Royal Statistical Society: Series B},
volume=68,
number=1,
pages={49--67},
year=2005,
}

@article{graphlasso,
title={Sparse inverse covariance estimation with the graphical lasso},
author={Jerome Friedman and Trevor Hastie and Robert Tibshirani},
journal={Biostatistics},
volume=9,
number=3,
pages={432--441},
year=2008,
}

@article{yuangraph,
title={Model selection and estimation in the {Gaussian} graphical model},
author={Ming Yuan and Yi Lin},
journal={Biometrika},
volume=94,
number=1,
pages={19--35},
year=2007,
}

@article{banerjeegraph,
title={Model selection through sparse maximum likelihood estimation for multivariate {Gaussian} or binary data},
author={Onureena Banerjee and Laurent El Ghaoui and Alexandre D'Aspremont},
journal={Journal of Machine Learning Research},
volume=9,
pages={485--516},
year=2008,
}

@article{lars,
title={Least angle regression},
author={Bradley Efron and Trevor Hastie and Iain Johnstone and Robert Tibshirani},
journal={Annals of Statistics},
volume=32,
number=2,
pages={407--499},
year=2004,
}

@article{lasso,
title={Regression shrinkage and selection via the lasso},
author={Robert Tibshirani},
journal={Journal of the Royal Statistical Society: Series B},
volume=58,
number=1,
pages={267--288},
year=1996,
}

@book{bert,
title={Nonlinear programming},
author={Dimitri P. Bertsekas},
publisher={Athena Scientific},
address={Nashua},
year={1999},
}

@article{meyerwood,
title={On the degrees of freedom in shape-restricted regression},
author={Mary Meyer and Michael Woodroofe},
journal={Annals of Statistics},
volume=28,
number=4,
pages={1083--1104},
year=2000,
}

@article{lassodf,
title={On the ``Degrees of Freedom" of the Lasso},
author={Hui Zou and Trevor Hastie and Robert Tibshirani},
journal={Annals of Statistics},
volume=35,
number=5,
pages={2173--2192},
year=2007,
}

@article{stein,
title={Estimation of the Mean of a Multivariate Normal Distribution},
author={Charles Stein},
journal={Annals of Statistics},
volume=9,
number=6,
pages={1135--1151},
year=1981,
}

@article{pco,
title={Pathwise coordinate optimization},
author={Jerome Friedman and Trevor Hastie and Holger Hoefling and Robert Tibshirani},
journal={Annals of Applied Statistics},
volume=1,
number=2,
pages={302--332},
year=2007,
}

@article{fuse,
title={Sparsity and smoothness via the fused lasso},
author={Robert Tibshirani and Michael Saunders and Saharon Rosset and Ji Zhu and Keith Knight},
journal={Journal of the Royal Statistics Society: Series B},
volume=67,
number=1,
pages={91--108},
year=2005,
}

@article{l1tf,
title={$\ell_1$ trend filtering},
author={Seung-Jean Kim and Kwangmoo Koh and Stephen Boyd and Dimitry Gorinevsky},
journal={SIAM Review},
volume=51,
number=2,
pages={339--360},
year=2009,
}

@book{convex,
title={Convex Optimization},
author={Stephen Boyd and Lieven Vandenberghe},
publisher={Cambridge University Press},
address={Cambridge},
year=2004,
}

@article{sure,
title={Adapting to unknown smoothness via wavelet shrinkage},
author={David L. Donoho and Iain Johnstone},
journal={Journal of the American Statistical Association},
volume=90,
number=432,
pages={1200--1224},
year=1995,
}

@article{cd,
title={Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization},
author={Paul Tseng},
journal={Journal of Optimization Theory and Applications},
volume=109,
number=3,
pages={475--494},
year=2001,
}

